You have $2,000 in your savings account that earns interest at a rate of 8% for 5 years. What is the amount of interest you would earn? *Remember, I = P x R x T

The correct statement about an odd function is:

B) It has line symmetry about the line y = –x.

Here we know that the function f(x) is an odd function, then we know that:

f(x) = -f(-x)

So, if we change the sign of the argument, we also change the sign of the of the output of the function, then there will be symmetry around the line:

y = -x

Then the correct option is B;

It has line symmetry about the line y = –x.

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So for question 24:

x = 47 degrees.

Triangles angles add to 180 degrees so 43 + 90 + 37 = 180.

y = 180 degrees.

A straight line is 180 degrees.

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Question 25:

x = 53 degrees.

X is similar to the angle that says 53 degrees.

y = 78 degrees.

180 - 49 - 53 - 79

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The y intercept of the line passes through the point (32, 22) and (48, 17) is 32

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ - y₁) / (x₂ - x₁)

The table shows that the line passes through the point (32, 22) and (48, 17). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-22=\frac{17-22}{48-32} (x-32)\\\\y=-\frac{5}{16}x+32[/tex]

The y intercept is 32

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Answer:

The y intercept of the line passes through the point (32, 22) and (48, 17) is 32

The number of solutions each equation has are one solution, No solution,  Infinitely many solutions.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

-1/2(12x-2)=-6x-1

1/2 (12x − 4) = 6x - 2

1/2 (12 x − 2) = −6x - 2

Now

-1/2(12x-2)=-6x-1; one solution

1/2 (12x − 4) = 6x - 2; No solution

1/2 (12 x − 2) = −6x - 2; Infinitely many solutions

Therefore, the solutions of the equations will be one solution, No solution,  Infinitely many solutions.

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The center of the circle is (13, 2)

The radius of the circle is 9

To find the center and radius of the circle described by the equation:

(x + 13)² + (y + 2)² = 81

We can compare with the standard form of the equation of the circle which is

(x - h)² + (y - k)² = r²

it can be deduced that

-h = 13, h = -13

-k = 2, k = -2

r² = 81, r = 9

This is the equation for a circle with center at (13, 2) and radius 9. So the center of the circle is (13, 2) and the radius is 9.

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Answer:

Center = (-13,-2)
Radius = 9

The percent of people that preferred vanilla ice cream is equal to 25%.

In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of people that prefer vanilla ice cream, we would develop an expression to multiply the fraction of the number of people by 100 as follows;

Number of people who prefer vanilla ice cream = 9/36 × 100

Number of people who prefer vanilla ice cream = 0.25 × 100

Number of people who prefer vanilla ice cream = 25%.

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The square root -6 -9 in complex number notation is √6i - 9

A complex number is a number of the form a + bi, where a and b are real numbers.

Given that, rewrite square root -6 -9 in complex number notation

We know that, the principal square root of a negative number is a positive number times i.

Therefore,

√-6 = √6i

Therefore, the mathematical notation will be

√6i - 9

Hence, the square root -6 -9 in complex number notation is √6i - 9

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Answer:

  (a)  3x +y = 2

Step-by-step explanation:

You want the equation y = -3x +2 written in standard form.

The standard form of a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.

To put the given equation into that form, we can add 3x to both sides:

  3x +y = 3x -3x +2

  3x +y = 2

I need a bat a hit ball with this sport.

The word "sport" refers to Baseball game.

Baseball is a team ball game played by two teams, namely the pitcher team and the batter team. The game begins when the pitcher throws the ball to the batter who is called the batter. Baseball is almost the same as softball, but the size of the tools used and the fields are different.

Baseball is included in small ball games and is often included in sports lessons at school. In order to play proper baseball, there are several rules that need to be observed. In addition, the complete protection needs to be met so that players can avoid injury.

Baseball game was first created in Coperstown, New York in 1883 by Abner Doubleday. But the first baseball rules made in 1845 by Alexander J. Cartwright.

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The polynomials that match with other equivalent expressions are :(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)

Consider the polynomials,

(a) 4x² + 18x                                (i) 2x(2x + 1)

(b) 4x² + 2x + 18x +9                   (ii) (2x + 1)(2x +9)

(c) (2x + 3)(2x + 3)                       (iii) 2x(2x + 9)    

(d) 4x² + 2x                                   (iv) 4x² + 12x + 9

Now,

Consider the polynomial 2x(2x + 1),

2x(2x + 1) = 2x(2x) + 2x(1)

2x(2x + 1) = 4x² + 2

Therefore, (d) is equal to (i).

Consider the polynomial 2x(2x + 9),

2x(2x + 9) = 2x(2x) + 2x(9)

2x(2x + 9) = 4x² + 18x

Therefore, (a) is equal to (iii).

Consider the polynomial (2x + 1)(2x +9) ,

(2x + 1)(2x +9)  = (2x)(2x) + (2x)(9) + (2x)(1) + 9

(2x + 1)(2x +9) = 4x² + 18x + 2x + 9

Therefore, (b) is equal to (ii).

Consider the polynomial (2x + 3)(2x + 3),

(2x + 3)(2x + 3) = (2x)(2x) + (2x)(3) + (3)(2x) + 9

(2x + 3)(2x + 3) = 4x² + 12x + 9

Therefore, (c) is equal to (iv).

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We can write the mathematical inequality as 3 ≤ (y - 2).

Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -

(ax + b) > (cx + d)

kx < 6

Given is the inequality statement as -

"3 less than or equal to symbol y - 2"

Mathematically, we can write the inequality statement as -

3 ≤ (y - 2)

Therefore, we can write the mathematical inequality as 3 ≤ (y - 2).

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The solution is Option D.

The sum of the infinite geometric progression is S = ( 64/7 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

S = 16 , -12 , 9 , -( 27/4 ) ...

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

a₁ = 16

a₂ = -12

So , the common ratio r = a₂ / a₁

The common ratio r = -3/4

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = 16 / ( 1 - ( -3/4 ) )

The sum of the infinite GP is S = 16 / ( 1 + 3/4 )

The sum of the infinite GP is S = 16 / ( 7/4 )

The sum of the infinite GP is S = ( 16 x 4 ) / 7

The sum of the infinite GP is S = ( 64/7 )

Hence , the sum of GP is ( 64/7 )

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Answer:

x = 11

y = 21

Step-by-step explanation:

1. y = 2x-1

2. 6x-2y = 24

lets plug in the value of y from the first equation, into the second

6x - 2(2x-1) = 24

6x - 4x + 2 = 24

2x + 2 = 24

2x = 22

x = 11

lets plug in x to the first equation to find y

y = 2(11)-1

y = 22-1

y = 21

Answer:

x = 11

y = 21

Step-by-step explanation:

y = 2x - 1;

6x - 2y = 24

y = 2x - 1

3x - y = 12

y = 2x - 1

3x - (2x - 1) = 12

y = 2x - 1

x + 1 = 12

y = 2x - 1

x = 11

y = 2(11) - 1

x = 11

y = 21

x = 11

The coordinates of point {B} would be (7,3).

Given is the point A(-3,-5) and its midpoint M(2,-1).

We can write as -

2 = (- 3 + x)/2

x - 3 = 4

x = 7

- 1 = (- 5 + y)/2

y - 5 = - 2

y = 3

Therefore, the coordinates of point {B} would be (7,3).

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The domain of the equation is equal to: B. all real numbers.

The range of the equation is equal to y ≥ -4 or {-4, ∞}.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or all real numbers.

Range = {-4, ∞} or {y|y ≥ -4}.

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Answer:

Step-by-step explanation:

In accordance with the Remainder theorem,  the given part means that the given polynomial has the roots of 1, -2 and 2.

So we write these three equations expressing this fact

   2A*1^4    - B*1^3    - C*1     - 16 = 0

   2A*(-2)^4 - B*(-2)^3 - C*(-2)  - 16 = 0

   2A*2^4    - B*2^3    - C*2     - 16 = 0

or

   2A -  B -  C = 16    (1)

  32A + 8B + 2C = 16    (2)

  32A - 8B - 2C = 16    (3)

Adding equations (2) and (3), you get

  64A           = 32,   which implies  A = 32%2F64 = 0.5.

Then from (1) and (2), substituting A = 0.5 there, you get

    B +  C = -15        (4)

   8B + 2C =   0        (5)

Expressing  B = -15 - C  from (4)  and substituting it to (5), you get

   8*(-15 -C) + 2C = 0,    or

   -120 - 8C +  2C = 0

        - 6C = 120

           C = - 20.

Then from equation (4),  B = -15 - (-20) = -15 + 20 = 5.

ANSWER.  A = 0.5;  B = 5,  C = -20.

We have three factors: (x-1),(x+2) and (x-2)

However, we have a quartic polynomial, since the degree (largest exponent) is 4

So we need a fourth factor. Let's call that x-p, for some real number p.

Let's expand out the following

(x-1)(x+2)(x-2)(x-p)

(x+2)(x-2)(x-1)(x-p)

(x^2-4)(x^2-px-x+p)

x^2(x^2-px-x+p)-4(x^2-px-x+p)

x^4-px^3-x^3+px^2-4x^2+4px+4x-4p

x^4+(-px^3-x^3)+(px^2-4x^2)+(4px+4x)-4p

x^4+(-p-1)x^3+(p-4)x^2+(4p+4)x-4p

Compare that result to 2Ax^4-Bx^3-Cx-16

Match up the corresponding terms, and we have the following equations

2Ax^4 = 1x^4 which leads to 2A = 1 and solves to A = 1/2 = 0.5

(-p-1)x^3 = -Bx^3 which leads -p-1 = -B and solves to B = p+1

(4p+4)x = -Cx which leads to 4p+4 = -C and solves to C = -4p-4

-4p = -16 which solves to p = 4

Use that value of p to find the other coefficients

B = p+1 = 4+1 = 5

C = -4p-4 = -4*4-4 = -20

The polynomial 2Ax^4-Bx^3-Cx-16 turns into x^4-5x^3+24x-16 after we plug in those A,B, and C values.

Answers:

A = 1/2 = 0.5

B = 5

C = -20

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Triangle BCD and triangle BML are similar by AA similarity. Therefore, option C is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure, ML║CD.

Consider ΔBCD and ΔBML

Here, ∠M=∠C (Corresponding angles are equal)

∠L=∠D (Corresponding angles are equal)

By AA similarity, ΔBCD ~ ΔBML

Therefore, option C is the correct answer.

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Let's call the sales tax rate as t (in decimal form).

The cost of a $10 sweater with the sales tax included is $10 + $10 * t = $10.90.

We can set up an equation to solve for t:

$10 * t = $0.90

Dividing both sides by $10:

t = 0.09

So the sales tax rate is 0.09, which is equivalent to 9%.

Answer: 116322

Step-by-step explanation:

23948+92374= 116322

The inverse relationship between the two variables is indicated by a negative slope. In this case, the y value falls as the x value rises. As an alternative, we may see that the y value rises as the x value falls.

You can tell if (0,0) is on the line if it crosses the origin. It is known that a line has a slope of m=0.5 if it is perpendicular to the equation y=2x+3. This is the slope's negative reciprocal. Using the provided information, solve for y=0.5x+b to get the answer.

A graph with a negative slope and a left-to-right tilt is produced by a declining linear function.

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Answer:

Below

Step-by-step explanation:

Interval is -1 to 2 = 3 units

value at -1     2(-1)^2 = 2

value at 2      2 (2^2) = 8      

  (8-2) / 3 = 6/3 = 2 /unit   rate of change

Answer:

Five divided by 206 is 0.02426

Answer:

41.2

Step-by-step explanation:

The ordered pair that completes the function is (0, 0)

From the question, we have the following parameters that can be used in our computation:

((15,21), (17,26). (21,37), (25,40), (30,45)

Missing pair = 1

Total pairs = 6

For a relation to be a function, the x values must point to different y values

This means that the pair (0, 0) can complete the function

This is so because it does not stop the relation from being a function

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The equation expressing the relationship between the amount of sale of statin, x years after 1998, S - 1.3·x = 5.5, indicates that the amount spent on statin in 2018 is $31,500,000,000

An equation expresses the relationship of equivalence between values or variables.

The equation that gives the amount of statin in billions of dollars is presented as follows;

Where;

S = The amount of sale of statin in billions of dollars

x = The number of years after 1998

The amount people in the U.S. will/did spend on statins in 2018 is found as follows;

S  = 1.3·x + 5.5

In 2018, x = 2018 - 1998 = 20

Therefore;

S  = 1.3 × 20 + 5.5 = 31.5

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Answer:

C

Step-by-step explanation:

The correct answer is C. Although Laura knew the creek was full of leeches, she pushed Nelly in anyway. Laura was tired of Nelly's arrogance and bragging.

The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

[tex](2x+1)+29=90\\2x+1=61\\2x=60\\x=30[/tex]

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Answer:

Andre's fraction of goals made to kicks taken is 4/6 or 2/3.

For Tom to make an equivalent fraction, he needs to make 4 goals out of a larger number of kicks than 6.

Two possible fractions for Tom would be 8/20 or 12/30. These both reduce to 2/5, which is equivalent to Andre's 2/3.

Answer: its either 6, 8, 2 or 8, 2. I don't know its one of these. bc ill show u how I got these.

Step-by-step explanation:

this could be:

plus,

times,

subtract,

or divide.

Answer:

  the direction changes if the coefficient is negative

Step-by-step explanation:

You want an explanation of the way you know the direction of the inequality symbol without solving the inequality.

If you have an inequality of the form ...

  ax < ( )

where the contents of ( ) has no terms containing x, then you know the solution is obtained by dividing both sides by 'a'.

You know that if 'a' is negative, that division will mean the inequality symbol is reversed:

  x > ( )/a . . . . . . . . for a < 0

When making this assessment, you only need to consider the sign of 'a', the coefficient of x. The rest of the inequality is immaterial.

__

Additional comment

Just as the sign of the variable coefficient tells you where the number line shading is relative to the boundary value, so the variable sign(s) can tell you where the shading is for a two-variable inequality.

For example, the inequality ...

  x -3y > 2

has a positive coefficient for x, so the shading will be to the right of the line (where x-values are greater than those on the boundary.)

The coefficient of y is negative, so this can be rewritten as ...

  y < ( )

meaning that shading is below the boundary line (where y-values are less than boundary values).

This inequality will have a boundary line with positive slope such that "right of the line" is the same as "below the line."

Answer:

c^2+4c-3

Step-by-step explanation:

(4c^2-3c^2)+(6c-2c)-3 = c^2+4c-3